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21 Sep 2021, 06:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
49% (02:42) correct
51%
(02:50)
wrong
based on 118
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If m is an integer greater than 1 and it divides \((7n+3)\) and also divides \((35n+26)\), what is the value of \(m\) ?
A. 3
B. 7
C. 10
D. 11
E. 13
A. 3
B. 7
C. 10
D. 11
E. 13
21 Sep 2021, 06:05
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Bunuel
m is a factor of both \((7n+3)\) and \((35n+26)\)
i.e. m is a factor of both \(5*(7n+3)\) and \((35n+26)\)
i.e. m is a factor of both \((35n+15)\) and \((35n+26)\)
i.e. \(m = (35n+26) - (35n+15) = 11\)
Answer: Option D
21 Sep 2021, 06:47
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Bunuel
If m is a factor of A and B, it is also a factor of A+B, A-B etc.
Here, m is a factor of A = (7n+3) and B = (35n+26)
Hence, m is a factor of B-A = 28n + 23 = C (say)
It is also a factor of C-A = 21n + 20 = D (say)
It is also a factor of D-A = 14n + 17 = E (say)
It is also a factor of E-A = 7n + 14 = F (say)
It is also a factor of F-A = 11
We did this step-by-step till we got rid of the n. We could have simply said that m is a factor of (B - 5A) and that would have got rid of n
Since 11 is prime and m is a factor of 11 (m > 1), we have: m = 11
Answer D
